Atoms are the building blocks of matter, but they're not the whole story. Inside atoms, we find protons, neutrons, and electrons, each playing a crucial role. These particles interact through fundamental forces, shaping the universe we see.

Nuclear reactions harness the energy locked inside atomic nuclei. By rearranging protons and neutrons through fusion or fission, we can convert tiny amounts of matter into enormous amounts of energy, powering stars and nuclear reactors alike.

Fundamental Particles and Nuclear Forces

Matter to energy conversion

• Einstein's famous equation $E = mc^2$ relates mass and energy
• Even a small amount of matter contains an immense amount of potential energy due to the speed of light squared ($c^2$)
• Nuclear reactions convert matter into energy by rearranging protons and neutrons (fusion combines lighter nuclei, fission splits heavier nuclei)
• Harnessing this energy has significant implications (nuclear power, atomic weapons)

Fundamental particles in atoms

• Protons carry positive charge and determine the element based on their number in the nucleus (hydrogen has 1, helium has 2, etc.)
• Neutrons are electrically neutral and provide stability to the nucleus by contributing to the strong nuclear force
• Electrons orbit the nucleus with negative charge and govern chemical properties (bonding, reactivity)
• Atomic nuclei consist of protons and neutrons held together by the strong nuclear force

Nuclear forces vs electrostatic repulsion

• Protons repel each other due to their like positive charges (electrostatic repulsion)
• However, at very short distances within the nucleus, the strong nuclear force overpowers this repulsion
• Neutrons enhance the strong force without adding electrostatic repulsion, allowing larger nuclei to form
• Stable nuclei exist when the strong force balances electrostatic repulsion (unstable nuclei undergo radioactive decay)

Nuclear Fusion and Energy Production in Stars

Sequence of solar fusion reactions

1. Hydrogen fusion: two protons combine to form deuterium (hydrogen-2), releasing a positron and neutrino
2. Deuterium fusion: a proton fuses with deuterium to create helium-3, emitting a gamma-ray photon
3. Helium-3 fusion: two helium-3 nuclei merge to produce helium-4 and two protons

• Net result: four protons become one helium-4 nucleus, with mass converted to energy
• These reactions occur in the Sun's core where temperatures reach 15 million ℃

Mass defects in stellar energy production

• Mass defect is the difference between a nucleus' mass and the sum of its individual proton and neutron masses
• This missing mass represents the binding energy holding the nucleus together
• In fusion, the product nucleus has less mass than the reactant nuclei
• The lost mass becomes energy according to $E = mc^2$, powering the star
• Stars balance inward gravitational force with outward fusion-generated pressure (hydrostatic equilibrium)
• Fusion of lighter elements into heavier ones continues until iron forms, as fusing iron consumes energy

Theory of Relativity and Spacetime

Special relativity

• Developed by Albert Einstein, special relativity describes how space and time are interconnected
• Introduces the concept of spacetime, a four-dimensional continuum combining three spatial dimensions with time
• Explains how the speed of light is constant for all observers, regardless of their relative motion

General relativity

• Einstein's theory of gravity that expands on special relativity
• Describes how massive objects curve spacetime, causing what we perceive as gravitational attraction
• Predicts phenomena such as gravitational time dilation and the bending of light by massive objects

Mass-energy equivalence

• The famous equation $E = mc^2$ stems from special relativity
• Distinguishes between rest mass (the mass of an object at rest) and the total mass-energy of a moving object
• Explains how particles can be created from pure energy in high-energy collisions